Conventionally, the process of using feedback to attenuate the level of additive noise and distortion in a particular frequency band, without attenuating the level of a signal in the same frequency band, is referred to as noise-shaping. Use of feedback to combine a corrupted output signal (i.e., an impaired output signal) with an underlying input signal, followed by subsequent processing, causes unwanted signal impairments to be filtered with one transfer function (i.e., a noise-transfer-function) while a desired input signal is filtered with a different transfer function (i.e., a signal-transfer-function). Typically, noise and distortion are shifted (i.e., shaped by the noise-transfer-function) into frequencies that lie outside the band of an underlying input signal (e.g., the band determined by the signal-transfer-function). The processing that produces this noise-shaped response is sometimes referred to as modulation, and the circuitry associated with this processing, is sometimes referred to as a modulator. Common uses of noise-shaping include data converters based on delta-sigma (ΔΣ) modulation and data converters based on diplexing-feedback-loops (DFLs), which conventionally are used to transform analog signals into representative digital samples.
Examples of conventional delta-sigma modulators 10A&B are illustrated in FIGS. 1A&B, respectively. Modulators 10A&B operate on continuous-time input signals, and therefore, are referred to as continuous-time delta-sigma (CT-ΔΣ) modulators. Such conventional CT-ΔΣ modulators produce a coarsely quantized version (e.g., digital samples on outputs 3A&B) of a continuous-time input signal (e.g., analog signals on inputs 1A&B), using a sampling rate which is many times the bandwidth of the input signal (i.e., the input signal is oversampled). As shown in FIGS. 1A&B, conventional CT-ΔΣ modulators include: 1) an input combining operation (e.g., within subtractors 7A&B); 2) an integration function of second-order (e.g., discrete integrators within shaping filters 9A&B); 3) a rounding/truncation function (e.g., within quantizing element 14); and 4) a feedback digital-to-analog (D/A) conversion function (e.g., within D/A converter 17). A variation of the CT-ΔΣ modulator is the discrete-time delta-sigma (DT-ΔΣ) modulator, which includes a sample-and-hold function at the modulator input, such that the modulator operates on the discrete-time samples of an input signal. Referring to FIGS. 1A&B, modulators 10A&B produce a signal-transfer-function HSTF (i.e., a transfer function from inputs 1A&B to outputs 3A&B, respectively) which is of the form
                    H        STF            ⁡              (        s        )              =                  ω        n        2                              s          2                +                  2          ⁢                                          ⁢                                    ζω              n                        ·            s                          +                  ω          n          2                      ,and produce a (quantization) noise-transfer-function HNTF (i.e., a transfer function from a virtual point of noise addition within quantizing element 14 to outputs 3A&B) which is of the form
            H      NTF        ⁡          (      s      )        =                    s        2                              s          2                +                  2          ⁢                                          ⁢                                    ζω              n                        ·            s                          +                  ω          n          2                      .  In addition to quantization noise, any other error or interference introduced onto the input (e.g., lines 4A&B) of quantizing element 14, or the output (e.g., lines 5A&B) of quantizing element 14, are subjected to this noise-transfer-function. The NTF produces a frequency response which is high-pass and similar to curve 18A shown in FIG. 1C, while the STF produces a frequency response that is lowpass and similar to curve 18B shown in FIG. 1C. Modulators (e.g., modulators 10A&B) having an NTF which is high-pass, conventionally are referred to as lowpass ΔΣ modulators and are utilized to attenuate the low-frequency quantization noise which is introduced by a coarse quantization operation (i.e., in the present examples, noise from quantizing element 14).
An alternative to the conventional ΔΣ modulator is the diplexing-feedback-loop (DFL) modulator, previously provided by the present inventor, e.g., as described in U.S. patent application Ser. No. 12/824,171 (now U.S. Pat. No. 8,089,382), Ser. No. 12/985,238 (now U.S. Pat. No. 8,299,947), Ser. No. 13/363,517 (now U.S. Pat. No. 8,943,112), Ser. No. 14/567,496 (now U.S. Pat. No. 9,209,829), Ser. No. 12/985,214 (now U.S. Pat. No. 8,416,111) and Ser. No. 14/558,640 (now U.S. Pat. No. 9,130,584), which are referred to herein as the “Related Patents” and are incorporated by reference herein as though set forth herein in full. An exemplary DFL is modulator 20, shown in FIG. 2. Like a conventional ΔΣ modulator, DFL modulator 20 produces an oversampled and coarsely quantized version of a continuous-time input signal (e.g., the input analog signal on line 1C), such that the quantization noise introduced by the coarse quantization operation (e.g., noise from quantizing element 14), is attenuated in a frequency band occupied by the input signal. Also, the DFL modulator is similar to a conventional ΔΣ modulator in that it does not appreciably attenuate the input signal itself. Rather than connecting the output of a combining operation (e.g., within adder 7C) to the input of a coarse quantization operation (e.g., quantizing element 14) through a filter transfer function (e.g., through integrators in a feed-forward path), however, the DFL modulator shapes noise by feeding back an error signal (i.e., signal 6C) which is generated through a linear combination of two feedback signals: 1) a filtered version of the input to the quantizing element (i.e., input signal 4C at node 13); and 2) a filtered version of the output from the quantizing element (i.e., output 5C). Since the DFL modulator does not rely on active integrators or filtering in a feed-forward path, the DFL modulator has significant performance advantages over a conventional ΔΣ modulator, including: 1) the DFL modulator is better suited for high-frequency operation because there are no active integrators which limit processing bandwidth; 2) the DFL modulator has an STF which is essentially all-pass because filtering takes place within a feedback path; and 3) the NTF of the DFL modulator is easily configured to exhibit band-stop responses as well as high-pass responses (i.e., the NTF can be configured to attenuate noise in a frequency band centered at other than zero hertz). Referring to the block diagram shown in FIG. 2, the linearized noise-transfer-function (NTF) produced by DFL modulator 20, is of the form
            NTF      ⁡              (        s        )              =                  1        +                                            H              1                        ⁡                          (              s              )                                ·                                    H              3                        ⁡                          (              s              )                                                  1        +                                            H              1                        ⁡                          (              s              )                                ·                                    H              3                        ⁡                          (              s              )                                      -                                            H              2                        ⁡                          (              s              )                                ·                                    H              3                        ⁡                          (              s              )                                            ,where it can be shown that for the appropriate choice of filter responses (e.g., H1, H2, and H3), DFL modulator 20 can produce a second-order, noise-shaped response that is comparable to that of a conventional ΔΣ modulator (e.g., modulators 10A&B). More specifically, an appropriate choice for the filter responses is:H1(s)·H3(s)=φ00·W00(s)+φ01·W01(s)H2(s)·H3(s)=φ10·W10(s)+φ11·W11(s),where φij are positive or negative scalars (i.e., gain terms) and Wij(s) are lowpass responses of first to fifth order. For the case where φ00=φ10=−2 and φ01=φ11=+1, the NTF produced by DFL modulator 20 is a high-pass response similar to curve 18A in FIG. 1C, and consequently, attenuates low-frequency noise. For other values of φij, the NTF produced by modulator 20 can be configured to produce a band-stop response with a spectral null at an arbitrary frequency fn, where φ00=−2·cos(2·7·fn/fS) and fS is the sampling rate of quantizing element 14. In addition to quantization noise, any error and/or interference introduced onto the input (e.g., line 4C) or the output (e.g., line 5C) of quantizing element 14 is subjected to this noise-transfer function.
Regardless of modulator type, maximum noise attenuation occurs when the stopband region associated with the noise-transfer-function of the modulator (e.g., DFL modulator 20) is closely aligned with the center frequency of a digital filter at the output of the modulator (e.g., output 3C of DFL modulator 20). The response of the digital filter is designed to pass the signal component from the output of the modulator to the output of the associated data converter, and reject the unwanted quantization noise that has been shaped to occupy a different frequency band from the signal. As illustrated by data converter 30A of FIG. 3A, a DFL modulator (e.g., modulator 19A comprising shaping filter 37, combiner 33, and quantizing element 34) is typically paired with a bandpass moving-average filter (e.g., filter 35), which like the modulator (e.g., modulator 19A), has a response that depends on programmable parameters. The passband region of bandpass filter 35 is established by digital values. The stopband region produced by the NTF of DFL modulator 19A, however, is a function of analog gain terms (i.e., scalar parameters φij), and consequently, the response of the DFL modulator is subject to component tolerances. To provide for maximum noise attenuation, therefore, as described in the Related Patents, the DFL converter (e.g., data converter 30A) can include a means of calibration that aligns the stopband produced by the NTF of the DFL modulator (e.g., modulator 19A) with the passband of the bandpass filter (e.g., filter 35).
DFL-based data converter 30A of FIG. 3A, employs a calibration (i.e., tuning) mechanism which includes a means for tuning the gain parameters (i.e., coefficients) of the DFL modulator (e.g., coefficients within shaping filter 37) according to the overall level at the output of the bandpass filter (e.g., bandpass moving-average filter 35). Since the shaped quantization noise at the output of quantizing element 34 is additive with respect to the input signal, the overall signal-plus-noise level at the output of bandpass filter 35 is proportional to the level of added quantization noise. The level of added quantization noise is minimum when the NTF response of modulator 19A is properly aligned with the response of bandpass filter 35, and therefore, the output of bandpass filter 35 provides a measure of NTF calibration (i.e., provides a tuning metric). More specifically, the added quantization noise is a minimum when the coefficients φij of shaping filter 37 are properly tuned, such that the NTF response exhibits a deep quantization noise null at the correct frequency (i.e., the center frequency of the bandpass filter response). Calibration within data converter 30A typically is such that the overall power (or signal strength) at the output of bandpass filter 35 is sensed using a square law operation (e.g., within detector 36), and then the coefficients of DFL shaping filter 37 are alternately adjusted, using an algorithm within processing block 38, until the overall power level (or signal-strength) at the output of bandpass filter 35 is forced to a minimum.
A second example of existing DFL calibration is that utilized by data converter 30B, shown in FIG. 3B. The calibration (i.e., tuning) within DFL-based data converter 30B adjusts the gain parameters of DFL shaping filter 37 according to a residual level of added quantization noise. Residual quantization noise is measured as the difference between the input of quantizing element 34 and the output of quantizing element 34, and is a minimum for a properly tuned DFL modulator. Referring to data converter 30B, a regressor signal ρ (i.e., on line 43) is generated from filter response W00(s) (i.e., within circuit 40A as shown, and/or within shaping filter 37), filter response W10(s) (i.e., within circuit 40B as shown, and/or within shaping filter 37), and adder 42 according to:ρ(t)=Qx(t)*W01−x(t)*W00,where: 1) the * operator represents linear convolution; 2) x(t) is the input to quantizing element 34; 3) Qx(t) is the quantized output of quantizing element 34; and 4) Wij are filter responses associated with shaping filter 37 of DFL modulator 19A. In the present exemplary converter, the calibration error on line 41 (i.e., the tuning metric) is generated from the regressor signal ρ(t) though a sequence of processing steps that include: 1) quantization via single-bit sampling/quantization circuit 44; 2) downconversion to baseband via mixer 47 and sinusoidal sequence 48; and 3) lowpass filtering via filter 49. Sinusoidal sequence 48 has a frequency (ωk) which corresponds to the intended center of a stopband response produced by the noise-transfer-function of modulator 19A. Using similar processing to DFL-based data converter 30A, the overall power (or signal strength) at the output of lowpass filter 49 is sensed using square law operation 36, and then using an algorithm within processing block 38, the coefficients of shaping filter 37 are alternately adjusted until the overall power level (or other measure of signal strength) at the output of lowpass filter 49 is forced to a minimum.
Each of the modulator calibration methods described above can be considered a passive approach, in that a calibration error is generated during a normal mode of operation, and does not involve the use of explicit reference signals (calibration waveforms) with deterministic (known) properties. These passive approaches can be advantageous from the standpoint of reducing potential disturbances to the normal operation of the data converter. However, the present inventor has determined that, compared to active calibration approaches, which employ explicit reference signals to provide a direct indication of tuning offsets, these passive approaches can result in less-optimal tuning (i.e., imperfect alignment of modulator and digital filter responses). For example, calibration errors based on a bandpass filter output can be confused by variations in signal power, because the output of the bandpass filter is a function of both signal power and quantization noise power. Calibration errors based on a measure of residual quantization noise (i.e., differences between the input and output of a quantizing element) are inherently noisy measurements, and therefore, can be unreliable indicators of optimal tuning. Consequently, the present inventor has determined that it is desirable to have improved methods for calibrating the responses of modulators which attenuate the level of unwanted noise and distortion in a particular frequency band, without similarly attenuating the level of a desired signal in the same frequency band.